ChapterChapter 22 FundamentalFundamental PropertiesProperties ofof AntennasAntennas

ECE 5318/6352 Antenna Engineering Dr. Stuart Long

1 .. IEEEIEEE StandardsStandards

. Definition of Terms for Antennas

. IEEE Standard 145-1983 . IEEE Transactions on Antennas and

Propagation Vol. AP-31, No. 6, Part II, Nov.

1983

2 ..RadiationRadiation PatternPattern (or(or AntennaAntenna Pattern)Pattern)

“The spatial distribution of a quantity which characterizes the electromagnetic field generated by an antenna.”

3 ..DistributionDistribution cancan bebe aa

. Mathematical function . Graphical representation . Collection of experimental data points

4 ..QuantityQuantity plottedplotted cancan bebe aa

. Power flux density W [W/m²] . Radiation intensity U [W/sr] . Field strength E [V/m] . Directivity D

5 . GraphGraph cancan bebe

. Polar or rectangular

6 . GraphGraph cancan bebe

. Amplitude field |E| or power |E|² patterns

(in linear scale) (in dB)

7 ..GraphGraph cancan bebe

. 2-dimensional or 3-D

most usually several 2-D “cuts” in principle planes

8 .. RadiationRadiation patternpattern cancan bebe

. Isotropic Equal radiation in all directions (not physically realizable, but valuable for comparison purposes)

. Directional Radiates (or receives) more effectively in some directions than in others

. Omni-directional nondirectional in azimuth, directional in elevation

9 ..PrinciplePrinciple patternspatterns . E-plane . H-plane Plane defined by H-field and Plane defined by E-field and direction of maximum direction of maximum radiation radiation

(usually coincide with principle planes of the coordinate system)

10 Coordinate System

Fig. 2.1 Coordinate system for antenna analysis. 11 ..RadiationRadiation patternpattern lobeslobes

. Major lobe (main beam) in direction of maximum radiation (may be more than one) . Minor lobe - any lobe but a major one . Side lobe - lobe adjacent to major one . Back lobe – minor lobe in direction exactly opposite to major one

12 ..SideSide lobelobe levellevel oror ratioratio (SLR)(SLR)

. (side lobe magnitude / major lobe magnitude) . - 20 dB typical . < -50 dB very difficult Plot routine included on CD for rectangular and polar graphs

13 PolarPolar PatternPattern

Fig. 2.3(a) Radiation lobes and beamwidths of an antenna pattern

14 LinearLinear PatternPattern

Fig. 2.3(b) Linear plot of power pattern and its associated lobes and beamwidths

15 ..FieldField RegionsRegions

. Reactive near field energy stored not radiated

D3 R  62.0 

λ= wavelength D= largest dimension of the antenna

16 ..FieldField RegionsRegions

. Radiating near field (Fresnel) radiating fields predominate

pattern still depend on R radial component may still be appreciable

D3 D2 62.0 R  2  

λ= wavelength D= largest dimension of the antenna

17 ..FieldField RegionsRegions

. Far field (Fraunhofer) field distribution independent of R field components are essentially transverse

D2 R  2 

18 ..RadianRadian

2 radians in full circle arc length of circle  r 

Fig. 2.10(a) Geometrical arrangements for defining a radian

19 ..SteradianSteradian

one steradian subtends an area of  rA 2

4π steradians in entire sphere

 2 sin ddrdA 

dA d  sin dd  r 2

Fig. 2.10(b) Geometrical arrangements for defining a steradian.

20 . RadiationRadiation powerpower densitydensity

. Instantaneous . Time average Poynting vector Poynting vector       1   HEW [ W/m ² ] Wavg Re  HE  [ W/m ² ] 2 [2-8] [2-3]

. Total instantaneous . Average radiated Power Power  [ W ]     Prad Wavg  d s  d sWP [ W ]  [2-9]  s s [2-4]

21 . RadiationRadiation intensityintensity

“Power radiated per unit solid angle”

2  WrU avg [W/unit solid angle]

2 r  2 U ),(  E r ),,( 2 2 r 2 2       rErE ),,(),,(  2 [2-12a] Note: This final equation does not 1 22   EEoo(,)  (,) have an r in it.   The “zero” 2   superscript means that the 1/r term is removed. far zone fields without 1/r factor 22

..DirectiveDirective GainGain

Ratio of radiation intensity in a given direction to the radiation intensity averaged over all directions

.Directivity Gain (Dg) -- directivity in a given direction

U U Dg  4 [2-16] Uo Prad

Prad (This is the radiation intensity if U0  the antenna radiated its power 4 equally in all directions.) 1 U , Note: 0  U sin dd 23 4 S ..DirectivityDirectivity

.Directivity -- Do

Umax Umax value of directive gain in Do  4 direction of maximum radiation Uo Prad intensity

Do (isotropic) = 1.0

0   DD og

24 ..BeamwidthBeamwidth

. Half power beamwidth Angle between adjacent points where field strength is 0.707 times the maximum, or the power is 0.5 times the maximum (-3dB below maximum)

. First null beamwidth Angle between nulls in pattern

Fig. 2.11(b) 2-D power patterns (in linear scale) of U()=cos²()cos³()

25 ..ApproximateApproximate directivitydirectivity forfor omnidirectionalomnidirectional patternspatterns

n    π For example U  sin  [2-32]     π .. McDonaldMcDonald .. PozarPozar

101 Do  1 2 Do   818.01914.172  0027.0HPBW  0027.0HPBW HPBW HPBW

[2-33a] Better if no minor lobes [2-33b]

(HPBW in degrees)

Results shown with exact values in Fig. 2.18

26 ..ApproximateApproximate directivitydirectivity forfor directionaldirectional patternspatterns

Antennas with only one narrow main lobe and very negligible minor lobes

   π/2 For example U  cosn  [2-31]    π .. KrausKraus .. TaiTai && PereiraPereira 441,253 Do  815,7218.22 Do   12rr 1 dd 2 2 2 2 2 1  2rr 1  2dd

[2-27] [2-30b]

( ) HPBW in two perpendicular planes in radians or in degrees) 1r ,2r 1d ,2d

Note: According to Elliott, a better number to use in the Kraus formula is 32,400 (Eq. 2-271 in Balanis). In fact, the 41,253 is really wrong (it is derived assuming a rectangular beam footprint instead of the correct elliptical one). 27 ..ApproximateApproximate directivitydirectivity forfor directionaldirectional patternspatterns

Can calculate directivity directly (sect.2.5), can evaluate directivity numerically (sect. 2.6)

(when integral for Prad cannot be done analytically, analytical formulas cannot be used )

28 ..GainGain

Like directivity but also takes into account efficiency of antenna (includes reflection, conductor, and dielectric losses)

4 Umax 4 Umax  eDeG ooooabs  [2-49c] Prad in (lossless,P isotropic source)

Efficiency  eeee dcro eo : overall eff. 2  ZZ oin  eee dccd er : reflection eff.  ;1   ZZ oin ec : conduction eff.

ed : dielectric eff.

P rad Prad eo  e  P cd inc Pin 29 ..GainGain

By IEEE definition “gain does not include losses arising from impedance mismatches (reflection losses) and polarization mismatches (losses)”

4 Umax DeG ocdo  [2-49a] in (lossless,P isotropic source)

30 ..BandwidthBandwidth

“frequency range over which some characteristic conforms to a standard”

. Pattern bandwidth . Beamwidth, side lobe level, gain, polarization, beam direction . polarization bandwidth example: circular polarization with axial

ratio < 3 dB

. Impedance bandwidth . usually based on reflection coefficient . under 2 to 1 VSWR typical

31 ..BandwidthBandwidth

. Broadband antennas usually use ratio (e.g. 10:1)

. Narrow band antennas usually use percentage (e.g. 5%)

32 ..PolarizationPolarization

. Linear . Circular . Elliptical

Right or left handed

rotation in time

33 ..PolarizationPolarization

.Polarization loss factor

2 2 PLF ˆˆwa cos p [2-71]

p is angle between wave and antenna polarization

34 ..InputInput impedanceimpedance

“Ratio of voltage to current at terminals of antenna”

ZA = RA + jXA

RA = Rr + RL

ZA = antenna impedance at terminals a-b

Rr = radiation resistance RL = loss resistance

35 ..InputInput impedanceimpedance

.. AntennaAntenna radiationradiation efficiencyefficiency

1 2 IRgr Power Radiated by Antenna Pr  2 ecd  Power Delivered to Antenna() PrL P 1122 IRgr IR gL 22

Rr ecd  [2-90]  RR Lr

Note: this works well for those antennas that are modeled as a series RLC circuit – like wire antennas. For those that are modeled as parallel RLC circuit (like a microstrip antenna), we would use G values instead of R values. 36 ..FriisFriis TransmissionTransmission EquationEquation

Fig. 2.31 Geometrical orientation of transmitting and receiving antennas for Friis transmission equation

37 ..FriisFriis TransmissionTransmission EquationEquation

2 Pr DD rrrttt ),(),( et = efficiency of transmitting antenna  ee rt 2 Pt 4 R er = efficiency of receiving antenna Dt= directive gain of transmitting antenna [2-117] Dr = directive gain of receiving antenna  = wavelength R = distance between antennas

assuming impedance and polarization matches

38 ..RadarRadar RangeRange EquationEquation

2 Pr DD rrrttt ),(),(      ee cdrcdt   Pt 4  4 RR 21 

Fig. 2.32 Geometrical arrangement of transmitter, target, and receiver for [2-123] radar range equation

39 ..RadarRadar CrossCross SectionSection RCS . Usually given symbol 

U . Far field characteristic  4 r Winc . Units in [m²]

Winc  incident power density on body from transmit direction

U r  scattered power intensity in receive direction

Physical interpretation: The radar cross section is the area of an equivalent ideal “black body” absorber that absorbs all incident power that then radiates it equally in all directions. 40 ..RadarRadar CrossCross SectionSection ((RCS)

. Function of . Polarization of the wave . Angle of incidence . Angle of observation . Geometry of target . Electrical properties of target . Frequency

41 ..RadarRadar CrossCross SectionSection ((RCS)

42